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Integral (cos x)^2 dx

by vadik
Tags: integral
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vadik
#1
Apr28-04, 04:36 PM
P: 23
Do any one have an idea how to calculate integral of (cos x)^2 ? Or is it even possible? I tried some substitutions and/or rules of trigonometry, like cosxcosx+sinxsinx=1, but it didn't help. Thank you!
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mathman
#2
Apr28-04, 04:42 PM
Sci Advisor
P: 6,039
cos2x+sin2x=1
cos2x-sin2x=cos2x
Therefore cos2x=(1+cos2x)/2

I'll let you finish.
vadik
#3
Apr28-04, 04:44 PM
P: 23
Thank you. :) integral (cos x)^2 dx

mussgo
#4
Mar3-08, 10:12 AM
P: 14
Integral (cos x)^2 dx

dont you have to use half angle identities to get integral of cos^2 ?
HallsofIvy
#5
Mar3-08, 12:00 PM
Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,345
No, double angle formulas as mathman said.
jacobrhcp
#6
Mar5-08, 03:01 PM
P: 169
an easy way to remember the solution to this common integral, when integrating over a whole period:

cos^2 x + sin ^2 x =1
[tex] \int cos^2 x = \int sin^2 x [/tex]
, at least when you integrate over a whole period

[tex] \int cos^2 x + \int sin^2 x =[/tex] length of a period

so the integral gives length of a period divided by 2
awvvu
#7
Mar5-08, 06:59 PM
P: 188
Why does this thread have over 16,000 views?

edit: Oh, it's four years old.
ohhohh
#8
Sep13-09, 12:20 AM
P: 1
First use the half-angle formula to change the cos(x)^2 to (1+cos(2x))/2...
This will allow you to break the integral into two seperate problems much easier to solve
integral{ 1/2dx + integral{ cos(2x)dx
Then you will have x/2 + (sin(2x)/2) + C
snipez90
#9
Sep13-09, 01:24 AM
P: 1,105
What the, that's not even correct. If you're gonna revive a 5-year old thread, at least make sure you don't have arithmetic errors.
chislam
#10
Sep14-09, 11:55 PM
P: 79
sin(2x)/4 ;)
abhishek2208
#11
Feb22-10, 05:35 AM
P: 1
use the euler's formula

cos x= [e^ix+e^-ix ]
[-------------]
[ 2 ]
sponsoredwalk
#12
Feb22-10, 06:20 AM
P: 532
http://www.5min.com/Video/An-Introdu...sine-169056088

Why doesn't the student, after nearly 6 years of unsuccessfully attempting this crazy integral, try a visual aid?
Redbelly98
#13
Feb22-10, 08:28 AM
Mentor
Redbelly98's Avatar
P: 12,070
This is crazy. The very first reply, post #2, answered the question. Six years ago!


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